arXiv subjects

Jatin Batra

Publications and source records attributed to Jatin Batra.

8 recordsLinked to original sources

arXiv2026

Convex Basins in Single-Index Model Loss Landscapes: Applications to Robust Recovery under Strong Adversarial Corruption

We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses. Prior work on robust recovery has considered settings such as linear regression (Pensia et al., JASA 2024), strictly monotonic link functions (Awasthi et al., NeurIPS 2022), and phase retrieval (Buna and Rebeschini, AISTATS 2025). However, these techniques do not extend to generic asymmetric non-monotonic link functions such as \textsc{GeLU} and \textsc{Swish}, which arise naturally as scalar primitives in modern gated neural architectures. We close this gap by giving the first robust recovery algorithm with near-linear sample and time complexity for generic non-monotonic link functions, thereby establishing the first robust recovery guarantees for a broad family of nonlinear SIMs for which \textit{no guarantees were previously known}. Our central contribution is a new structural understanding of the Gaussian squared-loss landscape under adversarial contamination. Crucially, we prove that for a broad class of nonlinear non-monotonic SIMs, a dimension-independent, constant-radius convex basin exists around the ground truth and is efficiently reachable via robust spectral initialization even under adversarial contamination. Prior works fail to establish both guarantees simultaneously, thereby either breaking down under adversarial contamination or failing to handle generic non-monotonic link functions. Together, these structural insights yield a principled warm start for robust gradient descent that provably converges to a final estimation error of $O(\sigma\sqrt{\epsilon})$ in $\tilde{O}(nd)$ time with $\tilde{O}(d)$ samples, where $\epsilon$ is the contamination fraction.

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arXiv2026

Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexity

Phase retrieval is the classical problem of recovering a signal $x^* \in \mathbb{R}^n$ from its noisy phaseless measurements $y_i = \langle a_i, x^* \rangle^2 + ζ_i$ (where $ζ_i$ denotes noise, and $a_i$ is the sensing vector) for $i \in [m]$. The problem of phase retrieval has a rich history, with a variety of applications such as optics, crystallography, heteroscedastic regression, astrophysics, etc. A major consideration in algorithms for phase retrieval is robustness against measurement errors. In recent breakthroughs in algorithmic robust statistics, efficient algorithms have been developed for several parameter estimation tasks such as mean estimation, covariance estimation, robust principal component analysis (PCA), etc. in the presence of heavy-tailed noise and adversarial corruptions. In this paper, we study efficient algorithms for robust phase retrieval with heavy-tailed noise when a constant fraction of both the measurements $y_i$ and the sensing vectors $a_i$ may be arbitrarily adversarially corrupted. For this problem, Buna and Rebeschini (AISTATS 2025) very recently gave an exponential time algorithm with sample complexity $O(n \log n)$. Their algorithm needs a robust spectral initialization, specifically, a robust estimate of the top eigenvector of a covariance matrix, which they deemed to be beyond known efficient algorithmic techniques (similar spectral initializations are a key ingredient of a large family of phase retrieval algorithms). In this work, we make a connection between robust spectral initialization and recent algorithmic advances in robust PCA, yielding the first polynomial-time algorithms for robust phase retrieval with both heavy-tailed noise and adversarial corruptions, in fact with near-linear (in $n$) sample complexity.

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arXiv2025

Comparing skill of historical rainfall data based monsoon rainfall prediction in India with NWP forecasts

The Indian summer monsoon is a highly complex and critical weather system that directly affects the livelihoods of over a billion people across the Indian subcontinent. Accurate short-term forecasting remains a major scientific challenge due to the monsoon's intrinsic nonlinearity and its sensitivity to multi-scale drivers, including local land-atmosphere interactions and large-scale ocean-atmosphere phenomena. In this study, we address the problem of forecasting daily rainfall across India during the summer months, focusing on both one-day and three-day lead times. We use Autoformers - deep learning transformer-based architectures designed for time series forecasting. These are trained on historical gridded precipitation data from the Indian Meteorological Department (1901--2023) at spatial resolutions of $0.25^\circ \times 0.25^\circ$, as well as $1^\circ \times 1^\circ$. The models also incorporate auxiliary meteorological variables from ECMWFs reanalysis datasets, namely, cloud cover, humidity, temperature, soil moisture, vorticity, and wind speed. Forecasts at $0.25^\circ \times 0.25^\circ$ are benchmarked against ECMWFs High-Resolution Ensemble System (HRES), widely regarded as the most accurate numerical weather predictor, and at $1^\circ \times 1^\circ $ with those from National Centre for Environmental Prediction (NCEP). We conduct both nationwide evaluations and localized analyses for major Indian cities. Our results indicate that transformer-based deep learning models consistently outperform both HRES and NCEP, as well as other climatological baselines. Specifically, compared to our model, forecasts from HRES and NCEP model have about 22\% and 43\% higher error, respectively, for a single day prediction, and over 27\% and 66\% higher error respectively, for a three day prediction.

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arXiv2025

A direct proof of a unified law of robustness for Bregman divergence losses

In contemporary deep learning practice, models are often trained to near zero loss i.e. to nearly interpolate the training data. However, the number of parameters in the model is usually far more than the number of data points n, the theoretical minimum needed for interpolation: a phenomenon referred to as overparameterization. In an interesting piece of work, Bubeck and Sellke considered a natural notion of interpolation: the model is said to interpolate when the model's training loss goes below the loss of the conditional expectation of the response given the covariate. For this notion of interpolation and for a broad class of covariate distributions (specifically those satisfying a natural notion of concentration of measure), they showed that overparameterization is necessary for robust interpolation i.e. if the interpolating function is required to be Lipschitz. Their main proof technique applies to regression with square loss against a scalar response, but they remark that via a connection to Rademacher complexity and using tools such as the Ledoux-Talagrand contraction inequality, their result can be extended to more general losses, at least in the case of scalar response variables. In this work, we recast the original proof technique of Bubeck and Sellke in terms of a bias-variance type decomposition, and show that this view directly unlocks a generalization to Bregman divergence losses (even for vector-valued responses), without the use of tools such as Rademacher complexity or the Ledoux-Talagrand contraction principle. Bregman divergences are a natural class of losses since for these, the best estimator is the conditional expectation of the response given the covariate, and include other practical losses such as the cross entropy loss. Our work thus gives a more general understanding of the main proof technique of Bubeck and Sellke and demonstrates its broad utility.

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arXiv2023

Simplicity Bias in 1-Hidden Layer Neural Networks

Recent works have demonstrated that neural networks exhibit extreme simplicity bias(SB). That is, they learn only the simplest features to solve a task at hand, even in the presence of other, more robust but more complex features. Due to the lack of a general and rigorous definition of features, these works showcase SB on semi-synthetic datasets such as Color-MNIST, MNIST-CIFAR where defining features is relatively easier. In this work, we rigorously define as well as thoroughly establish SB for one hidden layer neural networks. More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, we show that when the data is linearly separable, the network primarily depends on only the linearly separable ($1$-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenette and Waterbirds-Landbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

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arXiv2020

Non-uniform Geometric Set Cover and Scheduling on Multiple Machines

We consider the following general scheduling problem studied recently by Moseley. There are $n$ jobs, all released at time $0$, where job $j$ has size $p_j$ and an associated arbitrary non-decreasing cost function $f_j$ of its completion time. The goal is to find a schedule on $m$ machines with minimum total cost. We give an $O(1)$ approximation for the problem, improving upon the previous $O(\log \log nP)$ bound ($P$ is the maximum to minimum size ratio), and resolving the open question of Moseley. We first note that the scheduling problem can be reduced to a clean geometric set cover problem where points on a line with arbitrary demands, must be covered by a minimum cost collection of given intervals with non-uniform capacity profiles. Unfortunately, current techniques for such problems based on knapsack cover inequalities and low union complexity, completely lose the geometric structure in the non-uniform capacity profiles and incur at least an $Ω(\log\log P)$ loss. To this end, we consider general covering problems with non-uniform capacities, and give a new method to handle capacities in a way that completely preserves their geometric structure. This allows us to use sophisticated geometric ideas in a black-box way to avoid the $Ω(\log \log P)$ loss in previous approaches. In addition to the scheduling problem above, we use this approach to obtain $O(1)$ or inverse Ackermann type bounds for several basic capacitated covering problems.

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arXiv2020

Improved Approximations for Min Sum Vertex Cover and Generalized Min Sum Set Cover

We study the generalized min sum set cover (GMSSC) problem, wherein given a collection of hyperedges $E$ with arbitrary covering requirements $k_e$, the goal is to find an ordering of the vertices to minimize the total cover time of the hyperedges; a hyperedge $e$ is considered covered by the first time when $k_e$ many of its vertices appear in the ordering. We give a $4.642$ approximation algorithm for GMSSC, coming close to the best possible bound of $4$, already for the classical special case (with all $k_e=1$) of min sum set cover (MSSC) studied by Feige, Lovász and Tetali, and improving upon the previous best known bound of $12.4$ due to Im, Sviridenko and van der Zwaan. Our algorithm is based on transforming the LP solution by a suitable kernel and applying randomized rounding. This also gives an LP-based $4$ approximation for MSSC. As part of the analysis of our algorithm, we also derive an inequality on the lower tail of a sum of independent Bernoulli random variables, which might be of independent interest and broader utility. Another well-known special case is the min sum vertex cover (MSVC) problem, in which the input hypergraph is a graph and $k_e = 1$, for every edge. We give a $16/9$ approximation for MSVC, and show a matching integrality gap for the natural LP relaxation. This improves upon the previous best $1.999946$ approximation of Barenholz, Feige and Peleg. (The claimed $1.79$ approximation result of Iwata, Tetali and Tripathi for the MSVC turned out have an unfortunate, seemingly unfixable, mistake in it.) Finally, we revisit MSSC and consider the $\ell_p$ norm of cover-time of the hyperedges. Using a dual fitting argument, we show that the natural greedy algorithm achieves tight, up to NP-hardness, approximation guarantees of $(p+1)^{1+1/p}$, for all $p\ge 1$. For $p=1$, this gives yet another proof of the $4$ approximation for MSSC.

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arXiv2018

Constant Factor Approximation Algorithm for Weighted Flow Time on a Single Machine in Pseudo-polynomial time

In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call the Demand Multi-Cut problem. Even though we do not give a constant factor approximation algorithm for the Demand Multi-Cut problem on trees, we show that the specific instances of Demand Multi-Cut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.

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